Polar coordinates Definition and 587 Threads

Well, what I've done so far is calculating the magnitude of velocity and acceleration replacing ##t=2## in ##\theta (t)## and ##r(t)## so I could get the expressions for ##\dot r##, ##\dot \theta##, ##\ddot r## and ##\ddot \theta##. But that's not my problem... my problem is related to the...

Hello to all good people of physics forums. I just wanted to ask, whether the angular and linear (orbital) speed in perihelion of eliptical orbit are related the same way as in circular orbit (v = rw). If we take a look at the angular momentum (in polar coordinates) of reduced body moving in...

##{dx}^2+{dy}^2=3^2+3^2=18## ##{dr}^2+r^2{d\theta}^2=0^2+3^2*(\theta/2)^2\neq18## I have a feeling that what I'm doing wrong is just plugging numbers into the polar coordinate formula instead of treating it as a curve. For example, I naively plugged in 3 for r even though I know the radius...

I am labelling this as undergraduate because I got it from an undergraduate physics book (Tipler and Mosca). The uniform semicircle has radius R and mass M. I am getting the wrong answer but I can't see where I am going wrong. Any help would be appreciated. My solution: The centre of mass...

Summary: I can't figure out how the solver carries out the conversions from cartesian to cylindrical coordinates and vice-versa. I have a set of points of a finite element mesh which when inputted into a solver (ansys) gives the displacement of each node. I can get the displacement values of...

There is a simple geometric derivation of the area element ## r dr d\theta## in polar coordinates such as in the following link: http://citadel.sjfc.edu/faculty/kgreen/vector/Block3/jacob/node4.html Is there an algebraic derivation as well beginning with Cartesian coordinates and using ##...

Determine the polar coordinates of the two points at which the polar curves r=5sin(theta) and r=5cos(theta) intersect. Restrict your answers to r >= 0 and 0 <= theta < 2pi.

Say "I have grid in polar coordinates (r, theta). How do I plot it in tecplot. Tecplot plots it in cartesian coordinates."

Let $S^{n-1} = \left\{ x \in R^2 : \left| x \right| = 1 \right\}$ and for any Borel set $E \in S^{n-1}$ set $E* = \left\{ r \theta : 0 < r < 1, \theta \in E \right\}$. Define the measure $\sigma$ on $S^{n-1}$ by $\sigma(E) = n \left| E* \right|$. With this definition the surface area...

Hello, I get that both polar unit vectors, ##\hat{r}## and ##\hat{\theta}##, are unit vectors whose directions varies from point to point in the plane. In polar coordinates, the location of an arbitrary point ##P## on the plane is solely given in terms of one of the unit vector, the vector...

Homework Statement A particle of a mass ##m## is embedded in a circular rail, (radius: ##R##), without any friction. In a given moment, the particle finds itselfs without velocity at point C, and a force is applied on the rail, which starts moving with an ## \vec A ## constant acceleration. Use...

Homework Statement [/B] A particle is moving along a curve described by ##p(t) = Re^{\omega t}## and ##\varphi (t) = \omega t##. What is the particles transverse acceleration? Homework Equations [/B] None The Attempt at a Solution [/B] The position vector is ##Re^{\omega t} \vec{e_p}##...

Homework Statement Find the eigenfunctions and eigenvalues of the isotropic bidimensional harmonic oscillator in polar coordinates. Homework Equations $$H=-\frac{\hbar}{2m}(\frac{\partial^2}{\partial r^2}+\frac{1}{r}\frac{\partial}{\partial r}+\frac{1}{r^2}\frac{\partial^2}{\partial...

Hi, I have a general question. How do I show that an operator expressed in spherical coordinates is self adjoint ? e.g. suppose i have the operator i ∂/∂ϕ. If the operator was a function of x I know exactly what to do, just check <ψ|Qψ>=<Qψ|ψ> But what about dr, dphi and d theta

Could anyone please explain how can I know mathematically whether the logarithmic spiral curve spirals inward or outward? In which sense does the outward spiral spirals? Thank you very much for your help

Hello, I am in need of some clarification on tangential velocity in polar coordinates. As far as I know, the tangential velocity vector is ##\vec{v} = v\vec{e_t}##, where ##\vec{e_t} = \frac{\vec{v}}{v}##. This gives us the ##\vec{e_r}## and ##\vec{e_\varphi}## coordinates of the tangential...

Homework Statement Hello everyone, I have an assignment (Spivak's Calculus) to show that the polar equation of a hyperbola with the right focus in the origin is ##r=\frac {±\Lambda} {1+εcos(\theta)}##, but the equation I reached was slightly yet somewhat disturbingly different, and I'm not sure...

Homework Statement Graph the set of points whose polar coordinates satisfy the given equation or inequality. 0 ≤ θ ≤ , 0 ≤ r ≤ 4 Homework Equations - The Attempt at a Solution Is it correct ?

My question is why isn't the radial component e→r of acceleration in cylindrical coords simply r'' ? If r'' is the rate at which the rate of change of position is changing in the radial direction, wouldn't that make it the radial acceleration? I.e, the acceleration of the radius is the...

I am really confused about coordinate transformations right now, specifically, from cartesian to polar coordinates. A vector in cartesian coordinates is given by ##x=x^i \partial_i## with ##\partial_x, \partial_y \in T_p \mathcal{M}## of some manifold ##\mathcal{M}## and and ##x^i## being some...

Let's take two orthogonal curves in polar coordinates of the form ##\langle r,\theta \rangle##, say ##\langle r,0\rangle## and ##\langle r,\pi/2\rangle##. Cleary both lines are orthogonal, but the dot product is not zero. This must be since I do not have these vectors in the form ##\langle...

Homework Statement Question attached in attachments Homework Equations Area enclosed by polar graph is ∫0.5r^2 where r is the radius as a function of angle theta The Attempt at a Solution I attempted to use the formula above and I subtracted the area of the inside from the outside but it...

Homework Statement ##r=\frac 1 {cos(\theta)+1}## y=-x A region bounded by this curve and parabola is to be found. 2. The attempt at a solution I have found the points of intersection but I am not sure what to do with the line (I need polar coordinates and it is not dependent on r :( )...

Hey people, this question was already asked here [https://www.physicsforums.com/threads/velocity-in-plane-polar-coordinates.795749/], but I just couldn't understand the answer given, so I was wondering if some of you could help me by explaining it again. I don't really get Equation (or...

Homework Statement -infinity < r > +infinity Which of the following are equations for the line y=m*x for m<0: a. theta = -arctan(m) b. theta = arctan(m) c. theta = arctan(-m) d. theta = arctan(m) + pi e. theta = arctan(m) - pi f. r = 1/(sin(theta - arctan(m))) 2. The attempt at a solution...

Homework Statement I am trying to solve the axisymmetric diffusion equation for vorticity by Fourier transformation. Homework Equations $$ \frac{\partial \omega}{\partial t} = \nu \Big( \frac{1}{r}\frac{\partial \omega}{\partial r} + \frac{\partial^2 \omega}{\partial r^2} \Big). $$ The...

$\tiny{up(alt) 244.14.4.8}\\$ $\textsf{Describe the given region in polar coordinates}\\$ $\textit{a. Find the region enclosed by the semicircle}$ \begin{align*}\displaystyle x^2+y^2&=2y\\ y &\ge 0\\ \color{red}{r^2}&=\color{red}{2 \, r\sin\theta}\\ \color{red}{r}&=\color{red}{2\sin\theta}...

Any point on the plane can be specified with an ##r## and a ##\theta##, where ##\mathbf{r} = r \hat{\mathbf{r}}(\theta)##. From this, my book derives ##\displaystyle \frac{d \mathbf{r}}{dt}## by making the substitution ##\hat{\mathbf{r}}(\theta) = \cos \theta \hat{\mathbf{i}} + \sin \theta...

Homework Statement I tried to answer the following questions is about the curve surface z= f (x, y) = x^2 + y^2 in the xyz space. And the three questions related to each otherA.) Find the tangent plane equation at the point (a, b, a^2+ b^2) in curved surface z . The equation of the...

Hi, I'm getting into general relativity and am learning about tensors and coordinate transformations. My question is, how do you use the metric tensor in polar coordinates to find the distance between two points? Example I want to try is: Point A (1,1) or (sq root(2), 45) Point B (1,0) or...

Hey! :o Using polar coordinates I want to calculate $\iint_D \frac{1}{(x^2+y^2)^2}dxdy$, where $D$ is the space that is determined by the inequalities $x+y\geq 1$ and $x^2+y^2\leq 1$. We consider the function $T$ with $(x,y)=T(r,\theta)=(r\cos \theta, r\sin\theta)$. From the inequality...

< Mentor Note -- thread moved from the Homework physics forums to the technical math forums > Hello.I was reading recently barton's book.I reached the part corresponding to dirac-delta functions in spherical polar coordinates. he let :##(\theta,\phi)=\Omega## such that ##f(\mathbf...

Homework Statement 13.43 A child slides down the helical water slide AB. The description of motion in cylindrical coordinates is ##R=4m##, ##θ=ω^2t^2## and ##z=h[1-(\frac {ω^2t^2} {π})]##, where h=3m and ω=0.75rad/s. Compute the magnitudes of the velocity vector and acceleration vector when...

I need explanation of these formulas for polar coordinate system where position of an object is characterized by 2 vectors: r - from the origin to the object, and Φ - perpendicular to r, in the direction of rotation. https://drive.google.com/file/d/0ByKDaNybBn_eakJmS3dUVXVZUDA/view?usp=sharing...

Homework Statement 13.34 The curved portion of the cloverleaf highway interchange is defined by ##R^2=b^2sin2θ##, 0<=θ<=90deg. If a car travels along the curve at the constant speed v0, determine its acceleration at A Homework EquationsThe Attempt at a Solution [/B] Is this wrong?

Homework Statement 13.30 The colar B slides along a guide rod that has the shape of the spiral R = bθ. A pin on the collar slides in the slotted arm OC. If the speed of the collar is constant at v0, determine the angular speed ##\dot θ## of the arm OC in terms of v0, b, and θ. Homework...

Homework Statement 13.29 The colar B slides along a guide rod that has the shape of the spiral R = bθ. A pin on the collar slides in the slotted arm OC. If OC is rotating at the constant angular speed ##\dot θ = ω##, determine the magnitude of the acceleration of the collar when it is a A...

Homework Statement 13.25 The rod OB rotates counterclockwise about O at the constant angular speed of 45 rev/min while the collar A slides toward B with the constant speed 0.6 m/s, measured relative to the rod. When collar A is in the position R = 0.24m, θ = 0, calculate (a) its velocity...

Homework Statement 13.24 A particle travels along a plane curve. At a certain instant, the polar components of the velocity and acceleration are vR=90mm/s, vθ=60mm/s, aR=-50mm/s2, and aθ=20mm/s2. Determine the component of acceleration that is tangent to the path of the particle at this...

So when finding the Area from a double integral; or Volume from a triple integral: If the curve/surface has a negative region: (for areas, under the x axis), (for volumes, below z = 0 where z is negative) What circumstances allow the negative regions to be taken into account as positive when...

Homework Statement We've got an object/person in the center of a cicrcle that spins around with an angular velocity ω. That same object is moving at a constant speed k with the direction of the radius, that is from the center to the outside of the sphere. That object describes then a spiral...

15.3.65 Improper integral arise in polar coordinates $\textsf{Improper integral arise in polar coordinates when the radial coordinate r becomes arbitrarily large.}$ $\textsf{Under certain conditions, these integrals are treated in the usual way shown below.}$ \begin{align*}\displaystyle...

Homework Statement Find the divergence of the function ##\vec{v} = (rcos\theta)\hat{r}+(rsin\theta)\hat{\theta}+(rsin\theta cos\phi)\hat{\phi}## Homework Equations ##\nabla\cdot\vec{v}=\frac{1}{r^2}\frac{\partial}{\partial r}(r^2v_r)+\frac{1}{r sin\theta}\frac{\partial}{\partial...

Hi, on this page: https://en.wikipedia.org/wiki/Laplace_operator#Two_dimensions the Laplacian is given for polar coordinates, however this is only for the second order derivative, also described as \delta f . Can someone point me to how to represent the first-order Laplacian operator in polar...

Homework Statement question : find the value of \iint_D \frac{x}{(x^2 + y^2)}dxdy domain : 0≤x≤1,x2≤y≤x Homework Equations The Attempt at a Solution so here, i tried to draw it first and i got that the domain is region in first quadrant bounded by y=x2 and y=x and i decided to convert...

Hi, everyone. I had an example from my book, but I wasn't sure how they got \dfrac{1}{2}cos\theta on step 7? It seems like once they combined the constants, they ended up with just cos2\theta. Although, they have a \dfrac{1}{2} in front. Can someone help me understand where that constant came...

So I have this PDE: d2T/dr2 + 1/r dT/dr + d2T/dθ2 = 0. How do I implement dT/dr || [r = 0] = 0? Also, what should I do about 1/r? This is actually the first time I am going to attack FDF in polar/cylindrical coordinates. I can finite-difference the base equation fairly decently; I am just...

The 2D Laplacian in polar coordinates has the form of $$ \frac{1}{r}(ru_r)_r +\frac{1}{r^2}u_{\theta \theta} =0 $$ By separation of variables, we can write the ## \theta## part as $$ \Theta'' (\theta) = \lambda \Theta (\theta)$$ Now, the book said because we need to satisfy the condition ##...

Evaluate the double integral by converting to polar coordinates. Let S S be the double integral symbol S S xy dydx Inner limits: 0 to sqrt{2x - x^2} Outer limits: 0 to 2 The answer is 2/3. I know that x = rcosϴ and y = rsinϴ. S S rcosϴ*rsinϴ r drdϴ. S S (r^3)cosϴ*sinϴ drdϴ. I am stuck...